Radar Perene / Archive / science

Range, not point: how to read the output of a historical analogy model

◦ Index methodology v2.2 (working papers with DOI). See the methodology.

Science

There is a predictable moment in every presentation of a scenario model: someone in the audience asks for "the number". The model has just displayed a span of possible outcomes, and the first question is which one will happen — as if the span were a draft and the point the finished answer. The question is understandable and wrong in a specific way: it asks the model to erase precisely the information it produced.

The honest output of a historical analogy model is a span of scenarios with their frequencies — never a single number. The range is not the timid version of the answer; it is the answer. The point is a mutilation of it. That is how the historical analog engine under study at the house communicates any result, and the reason holds for any model of the kind.

An illustrative example, to give the idea a body

Imagine — the following values are invented to illustrate the format, not real outputs of the engine — that the current environment has half a dozen historical neighbors and that, in the months following those episodes, the market rose strongly in two cases, drifted sideways in three, and fell hard in one. The honest reading of that query has three layers, and none of them is a lone number.

The first layer is the span's width: from the strong-up outcomes to the strong-down one, the fan is wide — similar episodes ended far apart. The second is the internal shape: the most visited region was the tepid middle, not the headline-friendly extremes. The third is the size warning: six cases are six cases, and each carries one sixth of the portrait — enough to inform, not enough to nail down. Whoever compresses those three layers into "so it will drift sideways" has thrown away the width, the shape and the warning, and kept a prediction the model never made.

Why the point is a mutilation

The average of similar outcomes is a number easy to compute and almost always misleading to use. If half the neighbors preceded strong rallies and half preceded steep declines, the average points to a tepid "near zero" — an outcome that no episode in the sample produced. The midpoint of a two-humped fan describes a world that never existed; the span describes the two that did.

This is not an exotic defect of historical analogy — it is the same lesson classical statistics builds into confidence intervals: an estimate without its margin is incomplete information, and wide margins are not a failure of the method but a faithful portrait of a hard question. The difference is raw material: the confidence interval is born of a formula over a sample; the analogy's span is born of the raw collection of outcomes the past actually produced. In both cases, narrowing the span in communication, to sound more certain than one is, has a name: exaggeration.

How the house reads such an output

In internal practice, reading a query to the engine follows a deliberate order, and it can be described without a single real number. First, the width: is the fan narrow or wide? A wide fan is already a conclusion — it means the starting resemblance did not tame the outcomes, and that strong convictions about direction lack historical support. Then the shape: do the outcomes spread evenly, cluster in one region, split into two blocks? Each geometry tells a different story about the kind of uncertainty ahead. Last, and only last, some numerical summary — always accompanied by the case count that sustains it.

The order matters because it inverts the market's habit, which starts at the number and rarely reaches the width. Starting at the width is a vaccine: when the span is wide, no later summary can fake precision; when it is narrow, the summary arrives with its backing in view. What the reader will not find in any serious communication of the engine is the format "the model points to X" — because the model does not point; it apportions.

The reader as the last line of defense

Scenario models reach the public with growing frequency, and the mutilation into a point usually happens not in the model but in the retelling — the summary, the headline, the third-party commentary. The reader's defense fits in two questions: "what was the full span before this number?" and "how many cases support it?". When the answer to the first is silence and to the second is "few", the number inherited the fragility without inheriting the warning.

Frequently asked questions

Isn't a wide range the same as saying "I don't know"?

No. "I don't know" is an absence of information; the wide span is precise information about the size of the uncertainty — it says what the past produced from similar starting points and how far apart those outcomes landed. Knowing that no more can be known is knowledge, and an expensive kind.

Are the span's frequencies probabilities of the future?

They are frequencies of the past used as a declared approximation. Treating them as exact probabilities of the future would require assuming the environment has not changed — an assumption the next article in this trail examines head-on.

Why does the article's example use invented values?

Because the engine's real outputs belong to the draft study, and illustrating a format does not require exposing content. What the example teaches — width, shape, count — does not depend on the values.

Doesn't a manager ultimately need one number to act?

Deciding under a span is possible, and it is what any mature risk management does: the action is sized by the width of the fan, not by its center. The single point is not a prerequisite of the decision; it is a shortcut of communication.

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Continue the trail: Regime changes, analog changes: when comparing with the past stops making sense →

House reading: the historical outcomes that form any span are cataloged in the Atlas; the current reading, in the Diário.

Interpreting the output of one's own model by this ruler — width before center, count before conviction — is a conversation the house's bench has often.